Simplify the following expression: $ x = \dfrac{p + 10}{4} + \dfrac{-9}{10} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{10}{10}$ $ \dfrac{p + 10}{4} \times \dfrac{10}{10} = \dfrac{10p + 100}{40} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{-9}{10} \times \dfrac{4}{4} = \dfrac{-36}{40} $ Therefore $ x = \dfrac{10p + 100}{40} + \dfrac{-36}{40} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{10p + 100 - 36}{40} $ $x = \dfrac{10p + 64}{40}$ Simplify the expression by dividing the numerator and denominator by 2: $x = \dfrac{5p + 32}{20}$